Solving 2000x + 4000 = 24000: A Clear Step-by-Step Guide

Understanding how to solve linear equations like 2000x + 4000 = 24000 is essential for students, professionals, and anyone looking to strengthen their math skills. Whether you're tackling homework, preparing for exams, or simply curious, this article breaks down the equation step-by-step and explains how to simplify and solve it—along with a helpful real-world application.

Understanding the Context

What Is the Equation: 2000x + 4000 = 24000?

The equation 2000x + 4000 = 24000 is a linear equation in one variable. The goal is to isolate x to find its value. This type of equation appears frequently in algebra, finance, physics, and everyday problem-solving.

Step 1: Understand Each Part

2000x + 4000 = 24000

Key Insights

  • 2000x: The variable part—2000 multiplied by an unknown value x.
  • + 4000: A constant term added to the variable part.
  • = 24000: The equation states that the expression equals 24,000.

Step 2: Isolate the Variable Term

To simplify, first subtract 4000 from both sides to eliminate the constant on the left side:

2000x + 4000 − 4000 = 24000 − 4000
2000x = 20000

Continue Reading

A tank can be filled by Pipe A in 4 hours and by Pipe B in 6 hours. If both pipes are opened together, but Pipe B is closed after 2 hours, how long will it take to fill the tank?
Rate of Pipe A = \( \frac{1}{4} \) of the tank per hour
Rate of Pipe B = \( \frac{1}{6} \) of the tank per hour

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Final Thoughts

Step 3: Solve for x

Now divide both sides by 2000:

2000x ÷ 2000 = 20000 ÷ 2000
x = 10

✅ Final Answer:

x = 10

Why This Equation Matters

Equations like 2000x + 4000 = 24000 model real-life situations such as:

  • Budgeting: Planning a budget with fixed costs and variable expenses.
  • Distance & Time: Calculating travel time when speed and distance are known.
  • Physics: Solving for velocity, force, or resistances in simple circuits.